Jan. 20th, 2011
Building E, Room E1
12.00 a.m.
 

Selene Bianco

Dipartimento di Matematica, Universita' degli Studi di Torino

Mathematics has often been applied to study the behaviour of physical and biological processes and to make predictions. In the case of epidemiology it is possible to model the diffusion of a specific disease my means of the theory of dynamics of populations. In order to do it, a metapopulation has to be stratified into epidemic classes, representing the state of a group of individuals with respect to the disease. This subdivision has to take into account the natural history of the illness. For most of the childhood infectious diseases, the dynamics is well described by the classical susceptibles-exposed-infectious-recovered (SEIR) scheme.
However, the varicella zoster virus (VZV) does not disappear from the body after recovery from chickenpox, but A persists in the latent form in the sensory nerve ganglia and can be reactivated in the form of zoster. This complication force varicella models to be more complicated than a simple SEIR one.
The work that I am presenting here is about two ways of looking at mathematical models for childhood infectious diseases. A first one is purely theoretic and explores mathematical properties like the existence of an invariant measure on an epidemic stochastic process. The second one considers the practical case of varicella transmission by means of a deterministic model taking into account more details of the natural history of the disease.
In particular I will focus on the importance of choosing a good transmission pattern for the model and I will show the limits of simple deterministic models in capturing the main features of epidemics.